Because of its resistance to multipath channel fading and its spectral efficiency, orthogonal frequency division multiplexing (OFDM) has attracted increasing interest in recent years as a suitable modulation scheme for broadband wireless communication systems, including digital broadcasting and wireless LAN applications. OFDM is a method of digital modulation in which a signal is split into several narrowband channels at different frequencies. In some respects, OFDM is similar to conventional frequency-division multiplexing (FDM). Frequency division multiplexing (FDM) is a technology that transmits multiple signals simultaneously over a single transmission path, such as a cable or wireless system. Each signal travels within its own unique frequency range (carrier), which is modulated by the data (text, voice, video, etc.).
Orthogonal FDM's (OFDM) spread spectrum technique distributes the data over a large number of carriers that are spaced apart at precise frequencies. This spacing provides the “orthogonality” in this technique which prevents the demodulators from seeing frequencies other than their own. The benefits of OFDM are high spectral efficiency, resiliency to RF interference, and lower multi-path distortion. Since multiple versions of the signal interfere with each other (inter symbol interference (ISI)) it becomes very hard to extract the original information. Thus, priority is given to minimizing the interference among the channels and the symbols that make up the data stream.
Some basic definitions for digital signals are in order. A “data block” or “block of symbols” is a packet which includes a specified number of symbols. For instance, the IEEE 802.11a protocol specifies that each data block consists of 64 symbols. Since a digital signal can be represented in a simple way using a complex number, the real and imaginary parts determine a point in the two dimensional plane. The manner in which the signals (points) are laid out in the plane is referred to as a “signal constellation.” The number of points used for each particular modulation is the “constellation size” for that particular modulation.
OFDM is sometimes called multi-carrier or discrete multi-tone modulation. It is the modulation technique used for digital TV in Europe, Japan, and Australia. An OFDM signal is essentially a bundle of narrowband carriers transmitted in parallel at different frequencies from the same source; hence the phrase “multi-carrier” as opposed to “single carrier.” The individual carriers are commonly called subcarriers, and it is these subcarriers that transmit information via a modulation scheme. Typically, either PSK (phase shift keying) or QAM (quadrature amplitude modulation) schemes are used. The subcarriers are individually low symbol rate, with enough spacing between the subcarriers so that they are non-interfering. The spacing is typically designed as the inverse of the symbol duration, so that each subcarrier is orthogonal.
The multipath transmissions of the data block are received at different times due to the unequal path lengths of each path. Each transmission has a start time and a finish time for the data block. The difference between the finish times is the “channel length.” The “channel” is all the multiple paths that the signal with the data block actually takes. The signals from all the paths combine at the receiver to produce a distorted signal. The received signal is a convolution of the transmitted signal and the channel. The multipath signals can be modeled asx1(t)=a0s(t)+a1s(t−T)+a2s(t−2T) . . .x2(t)=b0s(t)+b1s(t−T)+b2s(t−2T) . . .
In OFDM, the channel is converted from a convolution to a multiplication which can be expressed as yk=H(k)dk which stands for y1=H(1)d1, y2=H(2)d2, . . . , where yk is a product between dk and H(k), where H(k) is the channel transfer function.
The cyclic prefix is a common feature of OFDM schemes which is used to combat ISI (inter symbol interference) and ICI (inter channel interference), which are introduced by the multipath channel that the signal takes between the transmitter and receiver. Cyclic prefix is the replication of part of the OFDM time-domain waveform to create a guard period. This part of the signal is added on by the transmitter and removed by the receiver. Once this is done, the signal model for the OFDM transmission over a multipath channel is simplified. The transmitted symbols at time slot l and subcarrier k are only disturbed by a factor Hl,k, which is the channel transfer function (the Fourier transform of the CIR (channel impulse response)) at the subcarrier frequency, as well as by additional white Gaussian noise n according tozl,k=αl,k·Hl,k+n so that the influence of the channel is removed by dividing by Hl,k. For a coherent OFDM system, reliable estimation of the time dispersive channel is the key to achieving the desired performance gain.
One method, the training symbol based OFDM method, usually requires an extra +20% bandwidth, thereby consuming too much of the available limited bandwidth.
Another method, the existing blind OFDM channel estimation method, is statistical in nature (e.g., it is second order statistics based as disclosed in B. Muquet and M. de Courville, “Blind and semi-blind channel identification methods using second order statistics for OFDM systems,” in Proc. International Conference on Acoustic Speech and Signal Processing, Phoenix, Ariz., March 1999, vol.5, pp. 2745-2748; X. Cai and A. N. Akansu, “A subspace method for blind channel identification in OFDM systems,” in Proc. ICC 2000, New Brunswick, N.J., March 2000, vol.2, pp. 929-933; X. Zhuang, Z. Ding, and A. L. Swindlehurst, “A statistical subspace method for blind channel identification in OFDM communications,” in Proc. 2000 International Conference on Acoustic Speech and Signal Processing, Istanbul, Turkey, June 2000, vol.5, pp. 2493-2496; and C. Li and S. Roy, “Subspace based blind channel estimation for OFDM by exploiting virtual carrier,” in Proc. CLOBECOM'01, San Antonio, Tex., November 2001, vol.1, pp. 295-299), which usually requires a large number of data blocks. Furthermore, this method has limited application in wireless channels involving high mobility (i.e., a large Doppler spread) as the channel may vary from block to block. The blind channel estimation methods have the advantage of higher bandwidth efficiency as they do not require the transmission of training symbols. However, they have limited applicability in wireless channels involving high mobility (large Doppler spread) as the channel may vary from block to block.
Yet another method, the deterministic blind channel estimation method, is more data efficient. For example, the finite-alphabet based method explored in N. Chotikakamthorn and H. B. Suzuki, “On identifiability of OFDM blind channel estimation,” in Proc. IEEE Vehicular Technology Conference, Amsterdam, Netherlands, September 1999 and S. Zhou and G. B. Giannakis, “Finite-alphabet based channel estimation for OFDM and related multicarrier systems,” IEEE Trans. Communications, pp. 1402-1414, August 2001 can be implemented using only a single data block. However, the developed algorithm is mostly limited in practice to PSK modulation.
The decision directed iterative algorithm was proposed in N. Chotikakamthorn and H. B. Suzuki, referred to above, for joint symbol and channel estimation. The performance, however, largely depends on the initial point and is subject to the error propagation effect. The proposed identifiability also hinges heavily upon the signal constellation. For example, for 16 QAM, the number of subcarriers should be at least 52 times the channel length, therefore having limited applicability in practice. In S. Zhou and G. B. Giannakis, referred to above, the finite alphabet is explicitly exploited to obtain an estimate of HJ(k) where H(k) is the channel frequency response at subcarrier k and J is a number determined by the signal constellation. While estimation of HJ(k) can be achieved using a single block for PSK modulation, multiple blocks are still required for QAM modulation along with some statistical assumptions on the input symbol. Further, to resolve the phase ambiguity in obtaining H(k) from HJ(k), the optimal minimum distance algorithm of S. Zhou and G. B. Giannakis requires a search of JN possible channels, which is usually prohibitive. Here J=4 for QAM modulation and J equals the constellation size for PSK modulation, while N is the number of subcarriers. Even the suboptimal phased directed algorithm can have substantial complexity for moderate to long channel lengths and is sensitive to the initial starting point of the iteration.
Receiver diversity is another important resource that can be exploited in OFDM channel estimation. As disclosed in H. Ali, J. H. Manton, and Y. Hua, “A SOS subspace method for blind channel identification and equalization in bandwidth efficient OFDM systems based on receive antenna diversity,” in Proc.11th IEEE Signal Processing Workshop on Statistical Signal Processing, Singapore, August 2001, pp. 401-404 and C. Li and S. Roy, “A subspace blind channel estimation method for OFDM systems without cyclic prefix,” in Proc. VTC'01 Fall, Atlantic City, N.J., October 2001, vol.4, pp. 2148-2152, multiple receive antennas are used for channel estimation for OFDM systems without cyclic prefix (CP).